A key to understanding complex biological systems such as cancer is to understand how networks of molecular interactions function in normal cells, and how they becomeperturbed in disease states. This endeavor demands sophisticated computational tools to derive and analyze molecular regulatory networks. Such tools need to integrate multiple types of data from high-throughput experiments to derive specific predictions - a systems biology approach. In this proposal we describe the development of novel machine learning methods to infer regulatory networks, that integrate known biology (prior information) with multiple types of high-throughput data. Our methods for inferring regulatory networks will be a key component of each biological project, and there will be an iterative feedback between the experimental and computational components to refine models and suggest new rounds of experiments. We will also develop computationally executable biological models that allow us to pose hypothetical what if questions to predict how a system will respond if we perturb it in a specific way, such as a therapeutic intervention. Phenotypic responses in cells can often be attained via more than one route, which is particularly problematic in cancer. A therapeutic regime may target a particular weakness in tumor cells, only for them to acquire additional mutations that elude the drug intervention by employing alternative pathways to achieve the same outcomes of survival and proliferation. We will develop multiscale models of cancer that estimate cellular level dynamics from tumor growth kinetics. Systems biology has benefited from utilizing methods originally developed in other disciplines for very different reasons. Major contributions have been made by applying methodologies from mathematics, statistics, computer science, engineering, and physics to biological questions. We plan to extend this interdisciplinary reach by adopting and developing ideas from the mathematics of geometry and topology in the identification of underlying patterns of progression in cancer, and to the analysis of large molecular networks.